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1.
Analytical solutions for some nonlinear evolution equations 总被引:1,自引:0,他引:1
IntroductionItiswell_knownthatmanyimportantdynamicsprocessescanbedescribedbyspecificnonlinearpartialdifferentialequations .Whenanonlinearpartialdifferentialequationisusedtodescribeaphysicalparameterthatshowssomekindsofpropagationoraggregationproperties,oneofthemostimportantphysicalmotivationsistosolvethepartialdifferentialequationwithacertaintypeoftravellingwavesolution .Inthepastseveraldecades,therehavebeenmanyattemptsinthisfieldbothbymathematiciansandphysicists[1]- [16 ],however,duetothecomp… 相似文献
2.
胡文瑞 《应用数学和力学(英文版)》1982,3(2):195-216
In this paper, the galactic spiral structure is studied by the galactic shock wave of interstellar gas with self-gravitation. The perturbed gravitation of stars is not a necessary condition for the existence of such shock. It is proved first of all that there exists solution of local shock wave even if the perturbed gravitation is absent. The condition |0|> is required for such solution. The spiral structure can only be explained by the shock solution when the difference of density between the regions of arm and interarm is larger. The grand design of shock wave with self-gravitation is obtained by the iterative method. The features of shock wave can be analyzed qualitatively in the velocity plane for a special perturbed gravitation which is used to simulate the self-gravitation of interstellar gas. As the mass distribution in proto- galactic disk is irregular initially, the grand design of the galactic shock wave was developed by the processes of winding, growth of instability and overlapping of waves. Hence, it gives a complete figure about the origin, evolution and persistance. A lot of observed phenomena and classificational features of the galactic spiral structure can be explained by adopting these ideas. 相似文献
3.
H. L. Abdel-Gawad 《Nonlinear dynamics》1995,8(3):307-314
We present a method for finding invariants of nonlinear differential equations of third order. Some propositions are given, which allow to conjecture the existence (or nonexistence) of invariants of a given nonlinear equation. As applications, invariants of the reduced Korteweg-de Vries and Nagumo equations, besides others, are studied. 相似文献
4.
IntroductionFindingsufficientconditionsfornonoscillatoryofsolutionsisaproblemofgeneralinterestinthetheoryofordinaryanddelaydifferentialequations.Inthisworkweconsiderdds σ(s) dds r(s) dxds +q(s) dxdsβ +p(s)xα =f(s) ,(1)whereσ ,r,q,pandfarereal_valuedcontinuousfuncti… 相似文献
5.
IntroductionInRef.[1 ] ,theauthorsestablishedtheuniqueexistenceofthesmoothsolutionforthefollowingcouplednonlinearequationsut=uxxx+buux+ 2vvx, (1 )vt=2 (uv) x. (2 )Thesewereproposedtodescribetheinteractionprocessofinternallongwaves.InRef.[2 ] ,ItoM .proposedarecursionoperatorbywhichheinferredthatEqs.(1 )and (2 )possesinfinitelymanysymmetriesandconstantsofmotion .InRef.[3 ] ,P .F .HeestablishedtheexistenceofasmoothsolutiontothesystemofcouplednonlinearKdVequation[4 ]ut=a(uxxx+buux) + 2bvvx,(… 相似文献
6.
Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations
of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used
to prove the convergence of the analytical formulas of the exact solutions of the equations. 相似文献
7.
For axially symmetric flows of dilatant granular materials, the velocity equations uncouple from the stress equations in certain plastic regimes, and assuming dilatant double shearing a closed set of three first-order partial differential equations are obtained. These supposedly simple equations are deceptive, because although they are simple in appearance, the determination of exact solutions is non-trivial. For one of the known families of solutions which has not been studied previously, the authors present the non-linear ordinary differential equation for the stress angle ψ and determine two small ψ approximations. Furthermore, the stream function and streamlines are obtained for ψ determined numerically and from the two small ψ approximations. For purposes of comparison, the streamlines for three further known exact solutions are also presented. In addition, we briefly examine the circumstances for which solutions of the velocity equations satisfy the principle of non-negative plastic work. For example, we are able to establish that in the case when the velocity equations are derived from a plastic potential, the solutions always satisfy the principle when the material has no cohesion. 相似文献
8.
INTEGRABLETYPESOFNONLINEARORDINARYDIFFERENTIALEQUATIONSETSOFHIGHERORDERSTangGuangsong(汤光宋)(MathematicsDepartment,JianghanUniv... 相似文献
9.
On a new algorithm of constructing solitary wave solutions for systems of nonlinear evolution equations in mathematical physics 总被引:2,自引:0,他引:2
IntroductionSolvingnonlinearequationsisalwaysaveryinterestingsubjectformathematicianandphysician ,inparticular,solitarywavesolutionsfornonlinearequationsareofboththeoreticalandpracticalimportance.Recently ,Yan[1]obtainedatransformationdirectlyfromthefamo… 相似文献
10.
乔宗椿 《应用数学和力学(英文版)》1991,12(7):697-704
In this paper we study the asymptotic expansions of the solutions for a class of secondorder ordinary differential equations with slowly varying coefficients.The defect of theknown works on these problems is noted,and the results in[1—4]are improved andextended by means of the modified method of multiple scales. 相似文献
11.
H.I. Abdel-Gawad 《International Journal of Non》2003,38(4):429-440
The polynomial invariants of (a set) non-linear differential equations are found by using a direct approach. The integrability of these invariants deserves the integrability of the given set of coupled differential equations. As applications, the Lorenz and Rikitake sets, among others, are studied. New invariants are obtained. 相似文献
12.
Numerical and analytical solutions of an Oldroyd 8‐constant MHD fluid with nonlinear slip conditions
The flow of an Oldroyd 8‐constant non‐Newtonian MHD fluid is investigated analytically and numerically. The governing equations for the flow field are derived for a steady one‐dimensional flow. The effect of constant applied magnetic field is included and its influence on the flow field is studied. The nonlinear governing equation along with nonlinear boundary conditions is solved analytically and the solution is obtained in an elegant way. Numerical solutions are also obtained using higher order Chebyshev spectral methods. The influence of various non‐Newtonian parameters and applied magnetic field is investigated. Results showing the effect of various physical parameters of the flow are presented and investigated. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, with the aid of computer symbolic computation system such as Maple, an algebraic method is firstly applied
to two nonlinear evolution equations, namely, nonlinear Schrodinger equation and Pochhammer–Chree (PC) equation. As a consequence,
some new types of exact traveling wave solutions are obtained, which include bell and kink profile solitary wave solutions,
triangular periodic wave solutions, and singular solutions. The method is straightforward and concise, and it can also be
applied to other nonlinear evolution equations in mathematical physics. 相似文献
14.
IntroductionandProblemintheResearchofToroidThispaperdealswiththeexistenceof2π_periodicsolutionstothenonlinearsystemoffirst_orderdifferentialequationswithadeviatingargument x(t) =Bx(t) F(x(t-τ) ) p(t) ,( 1 )wherex(t)∈R2 , x(t) =ddtx(t) ,τ∈R ,B∈R2×2 ,F :R2 →R2 isboundedandp∈C(… 相似文献
15.
靳明忠 《应用数学和力学(英文版)》1994,15(9):867-875
OSCILLATIONTHEOREMSOFHIGHERORDERNONLINEARDELAYDIFFERENTIALEQUATIONSJinMing-zhong(靳明忠)(DepartmentofBasicCourses,YunnanInstitut... 相似文献
16.
T. Candan 《应用数学和力学(英文版)》2006,27(10):1311-1320
Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given. 相似文献
17.
David E. Gilsinn 《Nonlinear dynamics》2007,50(1-2):73-92
In this paper, we prove a result that says: Given an approximate solution and frequency to a periodic solution of an autonomous
delay differential equation that satisfies a certain noncriticality condition, there is an exact periodic solution and frequency
in a neighborhood of the approximate solution and frequency and, furthermore, numerical estimates of the size of the neighborhood
are computed. Methods are outlined for estimating the parameters required to compute the errors. An application to a Van der
Pol oscillator with delay in the nonlinear terms is given. 相似文献
18.
In this paper, numerical solution of partial differential equations (PDEs) is considered by multivariate padé approximations. We applied these method to two examples. First, PDE has been converted to power series by two‐dimensional differential transformation, Then the numerical solution of equation was put into multivariate padé series form. Thus, we obtained numerical solution of PDE. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
A straightforward and concise method is proposed to construct special solutions of nonlinear diffusion equation. Many new
special solutions obtained. We believe this method is effective on solving other nonlinear differential equations. 相似文献
20.
Huang Yong-nian 《应用数学和力学(英文版)》1992,13(12):1115-1120
In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous
linear differential equations with constant coefficients and the n th-order homogeneous linear differential equation with
constant coefficients. In fact, we give the general formula for calculating the elements of the matrix exp [At]. We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better
than, the other methods. 相似文献